Chapter 14.9, Problem 13P

Verify the matrix equation $\left(\begin{array}{l}du\hfill \\ dv\hfill \end{array}\right)=\text{J}\left(\begin{array}{l}dx\hfill \\ dy\hfill \end{array}\right)$, where $\text{J}$ is a matrix whose determinant is the Jacobian in Problem 12. Multiply the matrix equation by its transpose and use Problem 12 to obtain $dS/ds=|dw/dz|$ as in (9.7).